In an old joke, two noblemen vie to name the bigger number. The first, afterruminating for hours, triumphantly announces “Eighty-three!” The second,mightily impressed, replies “You win.”

A biggest number contest is clearly pointless when the contestants taketurns. But what if the contestants write down their numbers simultaneously,neither aware of the other’s? To introduce a talk on “Big Numbers,” I invite twoaudience volunteers to try exactly this. I tell them the rules:

You have fifteen seconds. Using standard math notation, English words, orboth, name a single whole number—not an infinity—on a blank index card. Beprecise enough for any reasonable modern mathematician to determine exactly whatnumber you’ve named, by consulting only your card and, if necessary, thepublished literature.

So contestants can’t say “the number of sand grains in the Sahara,” becausesand drifts in and out of the Sahara regularly. Nor can they say “my opponent’snumber plus one,” or “the biggest number anyone’s ever thought of plusone”—again, these are ill-defined, given what our reasonable mathematician hasavailable. Within the rules, the contestant who names the bigger numberwins.

Are you ready? Get set. Go.

The contest’s results are never quite what I’d hope.

A fascinating look at big numbers. My kids have this “big number” contest pretty regularly and my daughter thinks she’s pretty clever when she trots out a gogol. From now on, I’m trumping her with BusyBeaver(7), even though I know I can do better. As a side note, my son usually goes with “eleventy hundred.”

Hat tip to @kottke.

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